A cubic-sum bound for variables of sum three

Proved

WorkbookSource.base_11249

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that for non-negative reals $a, b, c$ such that $a + b + c = 3$ , the inequality $7(a^2 + b^2 + c^2) \geq 2(c^3 + a^3 + b^3) + 9$ holds.

Source: InternLM Lean-Workbook, record lean_workbook_11249 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_11249 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hab : a + b + c = 3) : 7 * (a ^ 2 + b ^ 2 + c ^ 2) ≥ 2 * (c ^ 3 + a ^ 3 + b ^ 3) + 9  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_11249; Apache-2.0

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